Geometric Series, Infinate Series

Question

Video Link: https://www.101qs.com/2714

Watch the Stairs video above.

1. What is happening in the video?
2. Make a guess as to how many steps the person runs on the super stairs. 
3. Create a table or visual to represent the number of steps the person takes.

2. Using your visual, explain how to find the total number of steps and write a summation to determine the number of steps. Explain what type of series you used and why.

Part 2

Watch the Cell Division Video

Video Link: https://www.youtube.com/watch?v=KIpcCyuypzg&feature=youtu.be

2. Write an equation to describe cell division of bacteria at a given moment. Is this arithmetic or geometric? How do you know?

3. To find the number of bacteria in 5 hours, do you use the series formula or the sequence formula? Explain your answer. 

4. Find the number of bacteria that would grow in just 5 hours if they were not stopped?

Answer 1

For part one, he runs one stair, then two, then three, and so on, 21 times.

It is an arithmetic sequence, with common difference d = 1.

To find the total steps ran compute the series: Summation 1 to 21 n = (n+1)n/2, and substitute n = 21 obtaining 22(21)/2 = 231.